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57 (number)
57 (fifty-seven) is the natural number following 56 and preceding 58. It is a composite number.
In mathematics
57 is semiprime a Blum integer, and a Leyland number. The split Lie algebra E7 1⁄2 has a 57-dimensional Heisenberg algebra as its nilradical, and the smallest possible homogeneous space for E8 is also 57-dimensional. Although fifty-seven is not prime, it is jokingly known as the Grothendieck prime after a legend according to which the mathematician Alexander Grothendieck supposedly gave it as an example of a particular prime number. The joke is that he is famous for working abstractly, without concrete examples. However, while the veracity of this legend about Grothendieck is unclear, it is known that this very error was committed by another famous mathematician Hermann Weyl in a published article.
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